On the automorphism group of the p-adic group ring of a metacyclic p- group. II
In a recent paper [ibid. 82, 488-507 (1983; Zbl 0539.16006)] the author proved that for certain metacyclic p-groups G, \(Outcent(Z_ pG)=1\), where \(Z_ pG\) is the group ring of G over the ring of p-adic integers \(Z_ p\). Reference is made to the review of that paper for definitions. The purpose of the present paper is to extend the author's previous result to include all metacyclic p-groups, p an odd prime. Thus, the author proves: If G is a metacyclic p-group, p odd, then \(Outcent(Z_ pG)=1\). The author notes that it follows from this result that if G is any metacyclic p-group, p odd, then \(Outcent(Z_ qG)=1\) for any prime q.
scientific article; zbMATH DE number 3961872